How rotate the 3D view irrespective to the global Z axis using keyboard?
You can roll the view with Shift + Numpad 4 and Shift + Numpad 6.

Edit: Oops. This only works in turntable mode. I misunderstood the question. (Still investigating.)

Edit 2: Sorry. I couldn't figure it out. The best I can offer is this workaround:

Make the model a child of an empty, then rotate the empty 90º on the X axis. From there, you can view the top with Numpad 1 and orbit latitudinally with respect to the object with Numpad 4 and Numpad 6. Once you're done, you can delete the empty and the object will return to its pre-parented orientation.

This is not ideal because it might mess with the mechanics of an armature or other constraints or modifiers.